skip to main content

Title: Distinguishing d = 4 N = 2 SCFTs
We construct a family of examples of pairs of 4d N = 2 SCFTs whose graded Coulomb branch dimensions, Weyl-anomaly coefficients and flavour symmetry algebras and levels coincide, but which are nonetheless distinct SCFTs. The difference (detectable by the superconformal index) can occur at arbitrarily high order. We argue that it is, however, reflected in a difference in the global form of the flavour symmetry groups.  more » « less
Award ID(s):
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. We introduce a class of Higgs-branch RG flows in theories of class-S, which flow between d = 4 N = 2 SCFTs of the same ADE type. We discuss two applications of this class of RG flows: 1) determining the current-algebra levels in SCFTs where they were previously unknown — a program we carry out for the class-S theories of type E6 and E7 — and 2) constructing a multitude of examples of pairs of N = 2 SCFTs whose “conventional invariants” coincide. We disprove the conjecture of [1] that the global form of the flavour symmetry group is a reliable diagnostic for determining when two such theories are isomorphic. 
    more » « less
  2. A bstract We introduce a systematic approach to constructing $$ \mathcal{N} $$ N = 1 Lagrangians for a class of interacting $$ \mathcal{N} $$ N = 2 SCFTs. We analyse in detail the simplest case of the construction, arising from placing branes at an orientifolded ℂ 2 / ℤ 2 singularity. In this way we obtain Lagrangian descriptions for all the R 2 ,k theories. The rank one theories in this class are the E 6 Minahan-Nemeschansky theory and the C 2 × U(1) Argyres-Wittig theory. The Lagrangians that arise from our brane construction manifestly exhibit either the entire expected flavour symmetry group of the SCFT (for even k ) or a full-rank subgroup thereof (for odd k ), so we can compute the full superconformal index of the $$ \mathcal{N} $$ N = 2 SCFTs, and also systematically identify the Higgsings associated to partial closing of punctures. 
    more » « less
  3. We provide a new extension to the geometric construction of 6d (1, 0) SCFTs that encap- sulates Higgs branch structures with identical global symmetry but different spectra. In particular, we find that there exist distinct 6d (1, 0) SCFTs that may appear to share their tensor branch description, flavor symmetry algebras, and central charges. For example, such subtleties arise for the very even nilpotent Higgsing of (so4k,so4k) conformal matter; we pro- pose a method to predict at which conformal dimension the Higgs branch operators of the two theories differ via augmenting the tensor branch description with the Higgs branch chiral ring generators of the building block theories. Torus compactifications of these 6d (1, 0) SCFTs give rise to 4d N = 2 SCFTs of class S and the Higgs branch of such 4d theories are cap- tured via the Hall–Littlewood index. We confirm that the resulting 4d theories indeed differ in their spectra in the predicted conformal dimension from their Hall–Littlewood indices. We highlight how this ambiguity in the tensor branch description arises beyond the very even nilpotent Higgsing of (so4k,so4k) conformal matter, and hence should be understood for more general classes of 6d (1, 0) SCFTs. 
    more » « less
  4. A bstract We propose that the electroweak and flavour quantum numbers of the Standard Model (SM) could be unified at high energies in an SU(4) × Sp(6) L × Sp(6) R anomaly-free gauge model. All the SM fermions are packaged into two fundamental fields, Ψ L ∼ ( 4 , 6 , 1 ) and Ψ R ∼ ( 4 , 1 , 6 ), thereby explaining the origin of three families of fermions. The SM Higgs, being electroweakly charged, necessarily becomes charged also under flavour when embedded in the UV model. It is therefore natural for its vacuum expectation value to couple only to the third family. The other components of the UV Higgs fields are presumed heavy. Extra scalars are needed to break this symmetry down to the SM, which can proceed via ‘flavour-deconstructed’ gauge groups; for instance, we propose a pattern Sp(6) L → $$ {\prod}_{i=1}^3\mathrm{SU}{(2)}_{L,i}\to \mathrm{SU}{(2)}_L $$ ∏ i = 1 3 SU 2 L , i → SU 2 L for the left-handed factor. When the heavy Higgs components are integrated out, realistic quark Yukawa couplings with in-built hierarchies are naturally generated without any further ingredients, if we assume the various symmetry breaking scalars condense at different scales. The CKM matrix that we compute is not a generic unitary matrix, but it can precisely fit the observed values. 
    more » « less
  5. A bstract We derive explicit formulae to compute the a and c central charges of four dimensional $$ \mathcal{N} $$ N = 2 superconformal field theories (SCFTs) directly from Coulomb branch related quantities. The formulae apply at arbitrary rank. We also discover general properties of the low-energy limit behavior of the flavor symmetry of $$ \mathcal{N} $$ N = 2 SCFTs which culminate with our $$ \mathcal{N} $$ N = 2 UV-IR simple flavor condition . This is done by determining precisely the relation between the integrand of the partition function of the topologically twisted version of the 4d $$ \mathcal{N} $$ N = 2 SCFTs and the singular locus of their Coulomb branches. The techniques developed here are extensively applied to many rank-2 SCFTs, including new ones, in a companion paper. This manuscript is dedicated to the memory of Rayshard Brooks, George Floyd, Breonna Taylor and the countless black lives taken by US police forces and still awaiting justice. Our hearts are with our colleagues of color who suffer daily the consequences of this racist world. 
    more » « less